Our group focuses on using and developing accurate theoretical methods to study molecules, reactions, clusters, and extended systems. In particular, we specialize in ab initio (meaning "from the beginning") methods based on quantum mechanics, combining concepts and techniques from chemistry, physics, mathematics, and computer science.

In particular, we focus on development and application of coupled cluster techniques, including methods such as CCSD(T) which has been called the "gold standard" of quantum chemistry. Some of the basic questions that we seek to answer in our group include:

  • What benefits can ab initio quantum chemistry offer that complement experimental and semi-empirical techniques?
  • What are the limitations of quantum chemistry and how can it be combined with other computational methods?
  • How does explicit inclusion of quantum effects quantitatively and qualitatively impact molecular structure, dynamics, and reactivity?
  • How can experiments and theoretical calculations cooperatively inform each other?
  • How can advances in computational techniques drive theoretical and chemical developments?
Computational X-ray Spectroscopy

Spectroscopy is the study of the interaction of matter with light. In our context, this usually means studies of the absorption, emission, and scattering of light sources (usually lasers) by molecules, solids, and liquids. Theoretical methods can describe these interactions across a wide range of frequencies, providing diverse information on molecular structure and reactivity, from microwave (molecular geometry and rotation), to infrared (molecular vibration), and UV/visible (electronic transitions, chemical dynamics, reactivity) ranges.

We are working on extending these methods to the soft/tender X-ray region (100 eV-5 keV) of the spectrum, which exposes coupling of the core (1s) electrons in first- and second-row elements to the chemical environment. Using theoretical methods, we can compare to and explain measurements from many X-ray spectroscopic techniques such as NEXAFS (XANES), XES, XPS, and RIXS. These spectra contain a wealth of information on local chemical bonding and structure, vibronic coupling mechanisms, and reaction dynamics in high-energy processes.

Coupled cluster methods provide a systematically-improvable road to calculating the exact wavefunction of a system. Additionally, traditional coupled cluster methods have well-developed extensions for the calculation of molecular structure, properties, excited states, etc. However, the accuracy of coupled cluster is not without its cost, which limits application to very small systems for methods beyond CCSD. By developing suitable approximations, high-accuracy results can often be achieved with greatly reduced cost; an example is the CCSD(T) method for ground states.

We seek to develop approximate methods tailored to the calculation of advanced molecular features such as electronic excited states. The goal is to minimize cost and complexity while maximizing accuracy, theoretical consistency (such as size-extensivity), and compatibility with techniques such as analytical differentiation.

Development of Approximate Coupled Cluster Methods

When a core electron of a molecule is ionized or excited by X-ray radiation, the remaining core-hole induces significant relaxation (rearrangement) of the valence electrons. DFT methods have traditionally accounted for this effect either by using explicitly relaxed final-state orbitals (the ΔDFT method) or by using fractionally-occupied orbitals (TP-DFT). When using coupled cluster methods, electronic relaxation is handled by the electron correlation operator in an inefficient manner which limits accuracy.

We are investigating methods of explicitly treating core-hole relaxation in the coupled cluster framework along various lines.

Theoretical Treatment of Core-Hole Relaxation

Coupled cluster calculations depend critically on the computational efficiency of tensor operations. Tensors describe multi-dimensional data and transformations, such as electronic excitations from occupied to virtual orbitals. These tensor operations, primarily tensor contraction, have traditionally been implemented in terms of matrix operations, using highly-efficient routines such as provided by the BLAS. This approach comes with some unavoidable overhead, however, especially on emerging computational systems.

We have applied formal analysis methods developed for dense linear algebra in order to optimize tensor contraction and other operations without requiring an explicit tensor-to-matrix conversion. We are seeking to extend this approach to tensors with complex structures and symmetries encountered in coupled cluster calculations, as well as extensions to large scale out-of-core and distributed-memory calculations.

Computational Techniques for Tensor Contraction

Coupled cluster methods are notoriously expensive, scaling with systems size (e.g. number of electrons) as O(n^6) or worse. Recent developments in tensor factorization and low-rank representations have the promise to allow routine calculations with only O(n^4) scaling, or lower when combined with localization methods, all without sacrificing quantitative accuracy.

We are working on implementing these techniques for coupled cluster methods, including extensions to analytic derivatives, excited states, and higher-level correlation.

Reduced-Scaling Coupled Cluster Methods